CAMP (Computational, Applied Mathematics and PDE) Seminar

The seminar meets regularly on Wednesdays at 4pm in Eckhart 202. We also have special seminars during other days. This quarter the seminar will be running remotely via zoom. Access to the zoom links will be provided via the email list. To subscribe or unsubscribe from the email list, you may either go to Camp/PDE email list or contact Cornelia Mihaila.

Winter 2020 Schedule.

January 13
Mathieu Laurière, Princeton, Online, 4pm.
On Learning in Mean-Field Games
Mean-field game theory borrows ideas from statistical physics to provide a tractable approximation of very large multi-agent systems. Applications are ubiquitous in today's highly interconnected world, from crowd motion to macroeconomics and distributed robotics. Real-world problems often lead to models which are in high dimension or not fully specified, hence a recent surge of interest for the question of computing solutions with mesh-free and model-free methods. In this talk, we will mainly focus on the question of learning in mean-field games, in cooperative or non-cooperative settings.
January 20
Guilherme Mazanti, INRIA, Online, 4pm.
Minimal-time mean field games
Since their introduction around 2006, mean field games (MFGs) have been extensively studied and attracted the interest of many researchers from different backgrounds due to both their interesting mathematical properties and their applicability in a diversity of contexts. This talk will focus on some recent MFG models motivated by crowd motion, called minimal-time MFGs, in which agents want to minimize the time required to reach a given target set. In order to model congestion, the maximal speed of an agent is assumed to depend on the distribution of other agents around their position. After briefly presenting MFGs in general and minimal-time MFGs, the talk will review some recent results in two situations, corresponding to first-order MFGs, in which agents follow deterministic trajectories, and second-order MFGs, in which agents' trajectories are perturbed by additive Brownian motions, assumed to be mutually independent. We will present results on the existence of equilibria, their characterization, their asymptotic behavior, and their regularity properties. We will also discuss recent results which suggest how to tackle the case of minimal-time MFGs with state constraints. This talk is based on joint works with Romain Ducasse, Samer Dweik, Saeed Sadeghi Arjmand, and Filippo Santambrogio.

For questions, contact Cornelia Mihaila at: cmihaila [at] math [dot] uchicago [dot] edu.

Previous quarters:

Fall 2020 Spring 2020 Winter 2020 Fall 2019 Spring 2019 Winter 2019 Fall 2018 Spring 2018 Winter 2018 Fall 2017 Spring 2017 Winter 2017 Fall 2016 Spring 2016 Winter 2016 Fall 2015 Spring 2015 Winter 2015 Fall 2014 Spring 2014 Winter 2014 Fall 2013 Spring 2013 Winter 2013 Fall 2012 Spring 2012 Winter 2012 Fall 2011 Spring 2011 Winter 2011 Fall 2010 Spring 2010 Winter 2010 Fall 2009 Spring 2009